Betweenness

Betweenness is the property of lines in certain geometries, such as plane geometry, which allows one to talk about when a third point is between two points.

Betweenness does not hold in some geometries such as non-Euclidean geometry and the Fano plane. Betweenness is equivalent to the line being a linear order of its points. The concept of betweenness was first mathematically expressed by David Hilbert,[1] though the concept has naturally been used imprecisely in mathematics since at least the time of Euclid.